10th Science Formula Sheet: Physics & Biology Important Formulas.

Science Numerical Problem Formulae

10th Science - Quarterly Exam 2025 - Important Numerical Problem Formulae

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10th Science Formula Sheet

ELECTRICITY

Symbols and SI UNIT

Symbol	Quantity	SI Unit Symbol	SI Unit Name
I	Current	A	Ampere
Q	Charge	C	Coulomb
t	Time	s	Second
V	Potential Difference	V	Volt
W	Work	J	Joule
E	Energy	J	Joule
R	Resistance	Ω	Ohm
A	Area	m²	Unit² (meter square)
ρ	Resistivity	Ωm	Ohm.meter

Formulas

1. Current, Charge, and Time

\( I = \frac{Q}{t} \)

\( t = \frac{Q}{I} \)

\( Q = I \cdot t \)

2. Potential Difference, Work, and Charge

\( V = \frac{W}{Q} \)

\( Q = \frac{W}{V} \)

\( W = Q \cdot V \)

3. Ohm's Law

Potential difference is directly proportional to the current: \( V \propto I \)

\( V = I \cdot R \)

\( I = \frac{V}{R} \)

\( R = \frac{V}{I} \)

4. Factors Affecting Resistance

Resistance is directly proportional to length (l) and inversely proportional to the area of cross-section (A).

\( R \propto l \) and \( R \propto \frac{1}{A} \)

\( R = \rho \frac{l}{A} \)

5. Resistors in Series

\( R_s = R_1 + R_2 + R_3 + \dots \)

6. Resistors in Parallel

\( \frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots \)

7. Heat (Joule's Law of Heating)

\( H = I^2 R t \)

\( H = \frac{V^2}{R} t \)

\( H = V I t \)

8. Power

Note: Work (W) = Energy (E)

\( P = \frac{W}{t} \)

\( P = I^2 R \)

\( P = V I \)

\( P = \frac{V^2}{R} \)

9. Quantization of Charge

\( Q = n \cdot e \)

Where:
n → no. of electrons
e → charge on one electron (\(1.6 \times 10^{-19} C\))

LIGHT

1. Laws of Reflection

Angle of incidence = Angle of Reflection

\( \angle i = \angle r \)

2. Relation between Radius of Curvature and Focal Length

\( R = 2f \)

\( f = \frac{R}{2} \)

Where:
R = Radius of curvature
f = focal length

3. Mirror Formula

\( \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \)

Where:
v = distance of Image
u = distance of Object

4. Magnification (Mirrors)

\( m = \frac{h_i}{h_o} = \frac{v}{u} \)

Where:
hi = height of Image
ho = height of Object

5. Absolute Refractive Index

\( n = \frac{c}{v} \)

Where:
n = Index
c = velocity of light
v = velocity of light in medium

6. Relative Refractive Index

\( n_{21} = \frac{n_2}{n_1} \)

Also, \( n_{12} = \frac{n_1}{n_2} \)

Where:
n₂ = Speed of light in medium 2
n₁ = Speed of light in medium 1

7. Snell's Law

\( n_1 \sin i = n_2 \sin r \)

\( \Rightarrow \frac{\sin i}{\sin r} = \frac{n_2}{n_1} \)

8. Lens Formula

\( \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \)

9. Magnification (Lenses)

\( m = \frac{h_i}{h_o} = \frac{v}{u} \)

10. Power of a Lens

\( P = \frac{1}{f} \)

Where:
P = Power
f = focal length in meter

11. Power of Combination

\( P = P_1 + P_2 + P_3 + \dots \)

\( \frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} + \frac{1}{f_3} + \dots \)

MAGNETIC EFFECTS

The strength of the magnetic field (B) is related to:

Proportionality	Description
\( B \propto I \)	I = Current
\( B \propto \frac{1}{r} \)	r = Distance from Conductor
\( B \propto N \)	N = No. of turns

Where B = Magnetic field

Understanding Refraction of Light: Laws and Refractive Index | 10th Science Optics

Refraction of Light

REFRACTION OF LIGHT

When a ray of light travels from one transparent medium into another obliquely, the path of the light undergoes deviation. This deviation of ray of light is called refraction. Refraction takes place due to the difference in the velocity of light in different media. The velocity of light is more in a rarer medium and less in a denser medium. Refraction of light obeys two laws of refraction.

1. First law of refraction:

The incident ray, the refracted ray of light and the normal to the refracting surface all lie in the same plane.

2. Second law of refraction:

The ratio of the sine of the angle of incidence and sine of the angle of refraction is equal to the ratio of refractive indices of the two media. This law is also known as Snell’s law.

• Refractive index gives us an idea of how fast or how slow light travels in a medium. The ratio of speed of light in vacuum to the speed of light in a medium is defined as refractive index ‘µ’ of that medium.
• The speed of light in a medium is low if the refractive index of the medium is high and vice versa.
• When light travels from a denser medium into a rarer medium, the refracted ray is bent away from the normal drawn to the interface.
• When light travels from a rarer medium into a denser medium, the refracted ray is bent towards the normal drawn to the interface.

Optics Introduction | Class 10 Science Chapter 2 Explained

Optics - Introduction

Light is a form of energy which travels in the form of waves. The path of light is called ray of light and group of these rays are called as beam of light. Any object which gives out light are termed as source of light. Some of the sources emit their own light and they are called as luminous objects. All the stars, including the Sun, are examples for luminous objects. We all know that we are able to see objects with the help of our eyes. But, we cannot see any object in a dark room. Can you explain why? If your answer is ‘we need light to see objects’, the next question is ‘if you make the light from a torch to fall on your eyes, will you be able to see the objects?’ Definitely, ‘NO’. We can see the objects only when the light is made to fall on the objects and the light reflected from the objects is viewed by our eyes. You would have studied about the reflection and refraction of light elaborately in your previous classes. In this chapter, we shall discuss about the scattering of light, images formed by convex and concave lenses, human eye and optical instruments such as telescopes and microscopes.

Tags: Introduction, 10th Science : Chapter 2 : Optics

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Topic: 10th Science : Chapter 2 : Optics : Optics | Introduction